A refrigeration appliance includes a thermally insulating housing and a thermally insulating door. At least one of the housing and the door define an evacuated interspace and have an evacuated thermal insulation filling the interspace, a shaped, thermoplastic, substantially gas and water vapor impermeable outer cladding, and a shaped, thermoplastic, substantially gas and water vapor impermeable inner cladding. The inner cladding and the outer cladding substantially surround the interspace in a vacuum-tight manner. The cladding can be formed from polyolefins, polyvinylidene chloride, perfluoroalkoxy polymers. For reducing gas permeability, the cladding can be formed from ethylene/vinyl alcohol copolymer, polyacrylonitrile, and polyamide. The claddings can have co-extruded and/or laminated layers. The cladding can include a sputtered metal layer and/or a plastic/metal composite foil. The cladding can be formed from a thermoformed or blow-molded plastic. The insulation can have pressed silica or aerogel plates with a density of between 100 and 150 kg/m3.